Preprint / Version 1

We are the Champions

The Index for Evaluating Concentration of Championships Using a Sliding Window Approach


  • Ivan Simko



grouping of champions, individual sport, resampling, sliding windows, team sport, trends


The concept of competitive balance is considered to be an essential aspect in the field of sport economics. This work describes a novel approach for measuring and evaluating competitive balance through concentration of championships. The concentration of championships was assessed using a sliding window approach with the length of five consecutive competitions (years) and a single competition (year) increment over the whole evaluated period. Because the sliding window was relatively short, the newly developed index, termed ‘We Are the Champions’ (WAC5), is sensitive to rapid changes in competitive balance. The WAC5 index, average WAC5, expected WAC5, and ΔWAC5 were applied to data from 68 competitions of several individual and team sports collected for the 1960 – 2020 period. The significance of indices was tested by resampling (bootstrapping and permutation). The results of the study show a growth in competitive balance of several ice hockey competitions (national and international), but decreasing competitive balance in Formula 1 racing and in several European soccer competitions. In soccer competitions, there was a substantially lower competitive balance in a league than in a domestic cup competition within each country/federation. The difference between the overall competitive balance in the most popular, North American, professional leagues and the top European soccer leagues is growing. A significant grouping of champions was determined for all sports involving individual athletes, but also for several team competitions.